Moment inequalities for sums of certain independent symmetric random variables
P. Hitczenko; S. Montgomery-Smith; K. Oleszkiewicz
Studia Mathematica (1997)
- Volume: 123, Issue: 1, page 15-42
- ISSN: 0039-3223
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top- T. Figiel, P. Hitczenko, W. B. Johnson, G. Schechtman, and J. Zinn (1994), Extremal properties of Rademacher functions with applications to Khintchine and Rosenthal inequalities, Trans. Amer. Math. Soc., to appear. Zbl0867.60006
- T. Figiel, T. Iwaniec and A. Pełczyński (1984), Computing norms and critical exponents of some operators in -spaces, Studia Math. 79, 227-274. Zbl0599.46035
- E. D. Gluskin and S. Kwapień (1995), Tail and moment estimates for sums of independent random variables with logarithmically concave tails, ibid. 114, 303-309. Zbl0834.60050
- U. Haagerup (1982), Best constants in the Khintchine's inequality, ibid. 70, 231-283. Zbl0501.46015
- M. G. Hahn and M. J. Klass (1995), Approximation of partial sums of arbitrary i.i.d. random variables and the precision of the usual exponential bound, preprint.
- P. Hitczenko (1993), Domination inequality for martingale transforms of Rademacher sequence, Israel J. Math. 84, 161-178. Zbl0781.60037
- P. Hitczenko (1994), On a domination of sums of random variables by sums of conditionally independent ones, Ann. Probab. 22, 453-468. Zbl0809.60022
- P. Hitczenko and S. Kwapień (1994), On the Rademacher series, in: Probability in Banach Spaces, 9, Sandbjerg 1993, J. Hoffmann-Jørgensen, J. Kuelbs and M. B. Marcus (eds.), Birkhäuser, Boston, 1994, 31-36. Zbl0822.60013
- N. L. Johnson and S. Kotz (1970), Continuous Univariate Distributions, Houghton-Mifflin, New York. Zbl0213.21101
- W. B. Johnson, G. Schechtman and J. Zinn (1983), Best constants in moment inequalities for linear combinations of independent and exchangeable random variables, Ann. Probab. 13, 234-253. Zbl0564.60020
- M. Klass (1976), Precision bounds for the relative error in the approximation of and extensions, ibid. 8, 350-367. Zbl0428.60058
- S. Kwapień and J. Szulga (1991), Hypercontraction methods in moment inequalities for series of independent random variables in normed spaces, ibid. 19, 1-8. Zbl0718.60044
- S. Kwapień and W. A. Woyczyński (1992), Random Series and Stochastic Integrals. Single and Multiple, Birkhäuser, Boston. Zbl0751.60035
- M. Ledoux and M. Talagrand (1991), Probability in Banach Spaces, Springer, Berlin. Zbl0748.60004
- A. W. Marshall and I. Olkin (1979), Inequalities: Theory of Majorization and Its Applications, Academic Press, New York. Zbl0437.26007
- S. J. Montgomery-Smith (1990), The distribution of Rademacher sums, Proc. Amer. Math. Soc. 109, 517-522. Zbl0696.60013
- S. J. Montgomery-Smith (1992), Comparison of Orlicz-Lorentz spaces, Studia Math. 103, 161-189. Zbl0814.46023
- I. Pinelis (1994), Extremal probabilistic problems and Hotelling’s test under a symmetry condition, Ann. Statist. 22, 357-368. Zbl0812.62065
- I. Pinelis (1994), Optimum bounds for the distributions of martingales in Banach spaces, Ann. Probab. 22, 1679-1706. Zbl0836.60015
- H. P. Rosenthal (1970), On the subspaces of (p>2) spanned by sequences of independent random variables, Israel J. Math. 8, 273-303. Zbl0213.19303
- G. Schechtman and J. Zinn (1990), On the volume of the intersection of two balls, Proc. Amer. Math. Soc. 110, 217-224. Zbl0704.60017
- M. Talagrand (1989), Isoperimetry and integrability of the sum of independent Banach-space valued random variables, Ann. Probab. 17, 1546-1570. Zbl0692.60016
- S. A. Utev (1985), Extermal problems in moment inequalities, in: Limit Theorems in Probability Theory, Trudy Inst. Mat., Novosibirsk, 1985, 56-75 (in Russian).